548 lines
31 KiB
HTML
548 lines
31 KiB
HTML
<!DOCTYPE html>
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<title>复数算术</title>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-c_numeric_complex skin-cppreference2 action-view cpp-navbar">
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<div id="cpp-content-base">
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<div id="content"><a id="top"></a>
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<h1 id="firstHeading" class="firstHeading">复数算术</h1>
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<div id="contentSub"><span class="subpages">< <a href="c.html">c</a>‎ | <a href="c-numeric.html">numeric</a></span></div>
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<div id="mw-content-text" lang="zh" dir="ltr" class="mw-content-ltr" xml:lang="zh">
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<p>若实现定义了宏常量 <code>__STDC_NO_COMPLEX__</code> ，则不提供头文件 <code><complex.h></code> 、复数类型以及此处列出的所有名称。</p>
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</td>
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<td><span class="t-mark-rev t-since-c11">(C11 起)</span></td>
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<p>C 编程语言从 C99 开始支持三种内建类型 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">double</span> _Complex</span></span>、 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">float</span> _Complex</span></span> 及 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span> _Complex</span></span> 的复数数学运算（见 <a href="c-keyword-_Complex.html"><tt>_Complex</tt></a> ）。包含头文件 <code><complex.h></code> 时，三种复数类型亦可通过 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a></span></span>、 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">float</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a></span></span>、 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a></span></span> 使用。</p>
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<p>除了复数类型，还支持三种虚数类型： <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">double</span> _Imaginary</span></span>、 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">float</span> _Imaginary</span></span> 及 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span> _Imaginary</span></span> （见 <a href="c-keyword-_Imaginary.html"><tt>_Imaginary</tt></a> ）。包含头文件 <code><complex.h></code> 时，三种虚数类型亦可通过 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">double</span> <a href="c-numeric-complex-imaginary.html"><span class="kw745">imaginary</span></a></span></span>、 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">float</span> <a href="c-numeric-complex-imaginary.html"><span class="kw745">imaginary</span></a></span></span> 及 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span> <a href="c-numeric-complex-imaginary.html"><span class="kw745">imaginary</span></a></span></span> 使用。</p>
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<p>标准算术运算符 <span class="t-c"><span class="mw-geshi c source-c"><span class="sy2">+</span>, <span class="sy2">-</span>, <span class="sy2">*</span>, <span class="sy2">/</span></span></span> 可用于实数、复数及虚数类型的任意混合。</p>
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<p>推荐编译器定义 <code>__STDC_IEC_559_COMPLEX__</code> ，但并不强制要求其支持虚数。 POSIX 推荐检查是否定义宏 <span class="t-lc"><a href="c-numeric-complex-Imaginary_I.html">_Imaginary_I</a></span> 以鉴别是否支持虚数。</p>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span><br />
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<span class="t-mark-rev t-until-c11">(C11 前)</span></td>
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<p>若定义 <code>__STDC_IEC_559_COMPLEX__</code> <span class="t-rev-inl t-since-c23"><span>或 <code>__STDC_IEC_60559_COMPLEX__</code></span> <span><span class="t-mark-rev t-since-c23">(C23 起)</span></span></span> ，则支持虚数。</p>
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</td>
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<td><span class="t-mark-rev t-since-c11">(C11 起)</span></td>
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</tr>
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</table>
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<div>定义于头文件 <code><complex.h></code></div>
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<td colspan="2">
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<h5><span class="mw-headline" id=".E7.B1.BB.E5.9E.8B">类型</span></h5>
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</td>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-imaginary.html"><span class="t-lines"><span>imaginary</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>虚数类型宏<br />
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<span class="t-mark">(关键词宏)</span></td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-complex.html"><span class="t-lines"><span>complex</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>复数类型宏<br />
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<span class="t-mark">(关键词宏)</span></td>
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<td colspan="2">
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<h5><span class="mw-headline" id=".E8.99.9A.E6.95.B0.E5.B8.B8.E9.87.8F">虚数常量</span></h5>
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</td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-Imaginary_I.html"><span class="t-lines"><span>_Imaginary_I</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>虚数单位常量 i<br />
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<span class="t-mark">(宏常量)</span></td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-Complex_I.html"><span class="t-lines"><span>_Complex_I</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>复数单位常量 i<br />
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<span class="t-mark">(宏常量)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-I.html"><span class="t-lines"><span>I</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>复数或虚数单位常量 i<br />
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<span class="t-mark">(宏常量)</span></td>
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<td colspan="2">
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<h5><span class="mw-headline" id=".E6.93.8D.E4.BD.9C">操作</span></h5>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-CMPLX.html"><span class="t-lines"><span>CMPLX</span><span>CMPLXF</span><span>CMPLXL</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c11">(C11)</span></span><span><span class="t-mark-rev t-since-c11">(C11)</span></span><span><span class="t-mark-rev t-since-c11">(C11)</span></span></span></div>
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</div>
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</td>
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<td>由实部和虚部构建复数<br />
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<span class="t-mark">(宏函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-creal.html"><span class="t-lines"><span>creal</span><span>crealf</span><span>creall</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复数的实部<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-cimag.html"><span class="t-lines"><span>cimag</span><span>cimagf</span><span>cimagl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复数的虚部<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-cabs.html"><span class="t-lines"><span>cabs</span><span>cabsf</span><span>cabsl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复数的模（绝对值）<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-carg.html"><span class="t-lines"><span>carg</span><span>cargf</span><span>cargl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复数的辐角<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-conj.html"><span class="t-lines"><span>conj</span><span>conjf</span><span>conjl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算共轭复数<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-cproj.html"><span class="t-lines"><span>cproj</span><span>cprojf</span><span>cprojl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算黎曼球上的投影<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr>
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<td colspan="2">
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<h5><span class="mw-headline" id=".E6.8C.87.E6.95.B0.E5.87.BD.E6.95.B0">指数函数</span></h5>
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</td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-cexp.html"><span class="t-lines"><span>cexp</span><span>cexpf</span><span>cexpl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复数的 e 底指数<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-clog.html"><span class="t-lines"><span>clog</span><span>clogf</span><span>clogl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复数的自然对数<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr>
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<td colspan="2">
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<h5><span class="mw-headline" id=".E5.B9.82.E5.87.BD.E6.95.B0">幂函数</span></h5>
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</td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-cpow.html"><span class="t-lines"><span>cpow</span><span>cpowf</span><span>cpowl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复数幂函数<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-csqrt.html"><span class="t-lines"><span>csqrt</span><span>csqrtf</span><span>csqrtl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复数平方根<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr>
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<td colspan="2">
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<h5><span class="mw-headline" id=".E4.B8.89.E8.A7.92.E5.87.BD.E6.95.B0">三角函数</span></h5>
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</td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-csin.html"><span class="t-lines"><span>csin</span><span>csinf</span><span>csinl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复数正弦<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-ccos.html"><span class="t-lines"><span>ccos</span><span>ccosf</span><span>ccosl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复数余弦<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-ctan.html"><span class="t-lines"><span>ctan</span><span>ctanf</span><span>ctanl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复数正切<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-casin.html"><span class="t-lines"><span>casin</span><span>casinf</span><span>casinl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>计算复数反正弦<br />
|
|
<span class="t-mark">(函数)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="c-numeric-complex-cacos.html"><span class="t-lines"><span>cacos</span><span>cacosf</span><span>cacosl</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>计算复数反余弦<br />
|
|
<span class="t-mark">(函数)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="c-numeric-complex-catan.html"><span class="t-lines"><span>catan</span><span>catanf</span><span>catanl</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>计算复数反正切<br />
|
|
<span class="t-mark">(函数)</span></td>
|
|
</tr>
|
|
<tr>
|
|
<td colspan="2">
|
|
<h5><span class="mw-headline" id=".E5.8F.8C.E6.9B.B2.E5.87.BD.E6.95.B0">双曲函数</span></h5>
|
|
</td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="c-numeric-complex-csinh.html"><span class="t-lines"><span>csinh</span><span>csinhf</span><span>csinhl</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>计算复数双曲正弦<br />
|
|
<span class="t-mark">(函数)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="c-numeric-complex-ccosh.html"><span class="t-lines"><span>ccosh</span><span>ccoshf</span><span>ccoshl</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>计算复双曲余弦<br />
|
|
<span class="t-mark">(函数)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="c-numeric-complex-ctanh.html"><span class="t-lines"><span>ctanh</span><span>ctanhf</span><span>ctanhl</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>计算复数双曲正切<br />
|
|
<span class="t-mark">(函数)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="c-numeric-complex-casinh.html"><span class="t-lines"><span>casinh</span><span>casinhf</span><span>casinhl</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>计算复数反双曲正弦<br />
|
|
<span class="t-mark">(函数)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="c-numeric-complex-cacosh.html"><span class="t-lines"><span>cacosh</span><span>cacoshf</span><span>cacoshl</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>计算复数反双曲余弦<br />
|
|
<span class="t-mark">(函数)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="c-numeric-complex-catanh.html"><span class="t-lines"><span>catanh</span><span>catanhf</span><span>catanhl</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>计算复数反双曲正切<br />
|
|
<span class="t-mark">(函数)</span></td>
|
|
</tr>
|
|
</table>
|
|
<h3><span class="mw-headline" id=".E6.B3.A8.E8.A7.A3">注解</span></h3>
|
|
<p>下列函数名为 <code><complex.h></code> 的未来扩充而<span class="t-rev-inl t-since-c23"><span>潜在</span> <span><span class="t-mark-rev t-since-c23">(C23 起)</span></span></span>保留，并且在包含该头文件的程序中不可使用： <code>cerf</code>、 <code>cerfc</code>、 <code>cexp2</code> 、 <code>cexpm1</code>、 <code>clog10</code>、 <code>clog1p</code>、 <code>clog2</code>、 <code>clgamma</code>、 <code>ctgamma</code><span class="t-rev-inl t-since-c23"><span>、 <code>csinpi</code>、 <code>ccospi</code>、 <code>ctanpi</code>、 <code>casinpi</code>、 <code>cacospi</code>、 <code>catanpi</code>、 <code>ccompoundn</code>、 <code>cpown</code>、 <code>cpowr</code>、 <code>crootn</code>、 <code>crsqrt</code>、 <code>cexp10m1</code>、 <code>cexp10</code>、 <code>cexp2m1</code>、 <code>clog10p1</code>、 <code>clog2p1</code>、 <code>clogp1</code></span> <span><span class="t-mark-rev t-since-c23">(C23 起)</span></span></span> ，还有它们带 -f 及 -l 后缀的变体。</p>
|
|
<p>尽管 C 标准以“复弧双曲正弦（ complex arc hyperbolic sine ）”等名称指名反双曲函数，双曲函数的反函数却是面积函数。它们的参数是双曲扇形的面积，而非弧长。正确名称是“复反双曲正弦”等等。一些作者会使用“复面积双曲正弦（ complex area hyperbolic sine ）”等名称。</p>
|
|
<p>若组分的一部分是无穷大，则复数或虚数为无穷大，即使另一组分是 NaN 。</p>
|
|
<p>若双组分都不是无穷大或 NaN ，则复数或虚数是有限的。</p>
|
|
<p>若双组分皆为正零或负零，则复数或虚数为零。</p>
|
|
<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">示例</span></h3>
|
|
<div class="t-example">
|
|
<div class="t-example-live-link"></div>
|
|
<div dir="ltr" class="mw-geshi" style="text-align: left;">
|
|
<div class="c source-c">
|
|
<pre class="de1"><span class="co2">#include <stdio.h></span>
|
|
<span class="co2">#include <complex.h></span>
|
|
<span class="co2">#include <tgmath.h></span>
|
|
|
|
<span class="kw4">int</span> main<span class="br0">(</span><span class="kw4">void</span><span class="br0">)</span>
|
|
<span class="br0">{</span>
|
|
<span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> z1 <span class="sy1">=</span> I <span class="sy2">*</span> I<span class="sy4">;</span> <span class="co1">// 虚数单位平方</span>
|
|
<a href="c-io-fprintf.html"><span class="kw851">printf</span></a><span class="br0">(</span><span class="st0">"I * I = %.1f%+.1fi<span class="es1">\n</span>"</span>, <a href="c-numeric-complex-creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z1<span class="br0">)</span>, <a href="c-numeric-complex-cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z1<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
|
|
|
|
<span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> z2 <span class="sy1">=</span> <a href="c-numeric-math-pow.html"><span class="kw668">pow</span></a><span class="br0">(</span>I, <span class="nu0">2</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 虚数单位平方</span>
|
|
<a href="c-io-fprintf.html"><span class="kw851">printf</span></a><span class="br0">(</span><span class="st0">"pow(I, 2) = %.1f%+.1fi<span class="es1">\n</span>"</span>, <a href="c-numeric-complex-creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z2<span class="br0">)</span>, <a href="c-numeric-complex-cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z2<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
|
|
|
|
<span class="kw4">double</span> PI <span class="sy1">=</span> <a href="c-numeric-math-acos.html"><span class="kw673">acos</span></a><span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span>
|
|
<span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> z3 <span class="sy1">=</span> <a href="c-numeric-math-exp.html"><span class="kw657">exp</span></a><span class="br0">(</span>I <span class="sy2">*</span> PI<span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 欧拉公式</span>
|
|
<a href="c-io-fprintf.html"><span class="kw851">printf</span></a><span class="br0">(</span><span class="st0">"exp(I*PI) = %.1f%+.1fi<span class="es1">\n</span>"</span>, <a href="c-numeric-complex-creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z3<span class="br0">)</span>, <a href="c-numeric-complex-cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z3<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
|
|
|
|
<span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> z4 <span class="sy1">=</span> <span class="nu0">1</span><span class="sy2">+</span><span class="nu0">2</span><span class="sy2">*</span>I, z5 <span class="sy1">=</span> <span class="nu0">1</span><span class="sy2">-</span><span class="nu0">2</span><span class="sy2">*</span>I<span class="sy4">;</span> <span class="co1">// 共轭</span>
|
|
<a href="c-io-fprintf.html"><span class="kw851">printf</span></a><span class="br0">(</span><span class="st0">"(1+2i)*(1-2i) = %.1f%+.1fi<span class="es1">\n</span>"</span>, <a href="c-numeric-complex-creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z4<span class="sy2">*</span>z5<span class="br0">)</span>, <a href="c-numeric-complex-cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z4<span class="sy2">*</span>z5<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
|
|
<span class="br0">}</span></pre></div>
|
|
</div>
|
|
<p>输出：</p>
|
|
<div dir="ltr" class="mw-geshi" style="text-align: left;">
|
|
<div class="text source-text">
|
|
<pre class="de1">I * I = -1.0+0.0i
|
|
pow(I, 2) = -1.0+0.0i
|
|
exp(I*PI) = -1.0+0.0i
|
|
(1+2i)*(1-2i) = 5.0+0.0i</pre></div>
|
|
</div>
|
|
</div>
|
|
<h3><span class="mw-headline" id=".E5.BC.95.E7.94.A8">引用</span></h3>
|
|
<div class="t-ref-std-17">
|
|
<ul>
|
|
<li>C17 标准（ISO/IEC 9899:2018）：</li>
|
|
</ul>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>6.10.8.3/1/2 <code>__STDC_NO_COMPLEX__</code> (p: 128)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>6.10.8.3/1/2 <code>__STDC_IEC_559_COMPLEX__</code> (p: 128)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.3 Complex arithmetic <code><complex.h></code> (p: 136-144)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.25 Type-generic math <code><tgmath.h></code> (p: 272-273)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.31.1 Complex arithmetic <code><complex.h></code> (p: 391)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>Annex G (normative) IEC 60559-compatible complex arithmetic (p: 469-479)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
</div>
|
|
<div class="t-ref-std-11">
|
|
<ul>
|
|
<li>C11 标准（ISO/IEC 9899:2011）：</li>
|
|
</ul>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>6.10.8.3/1/2 <code>__STDC_NO_COMPLEX__</code> (p: 177)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>6.10.8.3/1/2 <code>__STDC_IEC_559_COMPLEX__</code> (p: 177)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.3 Complex arithmetic <code><complex.h></code> (p: 188-199)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.25 Type-generic math <code><tgmath.h></code> (p: 373-375)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.31.1 Complex arithmetic <code><complex.h></code> (p: 455)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>Annex G (normative) IEC 60559-compatible complex arithmetic (p: 532-545)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
</div>
|
|
<div class="t-ref-std-c99">
|
|
<ul>
|
|
<li>C99 标准（ISO/IEC 9899:1999）：</li>
|
|
</ul>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>6.10.8/2 <code>__STDC_IEC_559_COMPLEX__</code> (p: 161)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.3 Complex arithmetic <code><complex.h></code> (p: 170-180)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.22 Type-generic math <code><tgmath.h></code> (p: 335-337)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.26.1 Complex arithmetic <code><complex.h></code> (p: 401)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>Annex G (informative) IEC 60559-compatible complex arithmetic (p: 467-480)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
</div>
|
|
<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">参阅</span></h3>
|
|
<table class="t-dsc-begin"></table>
|
|
</div>
|
|
<div class="visualClear"></div>
|
|
</div>
|
|
</div>
|
|
</div>
|
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</body>
|
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</html>
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